This website is hosted on a server, but it is not, by itself, considered a server. A server is simply a computer that provides services to a client, whereas a website is just one of the many things a server can serve. For example, a server might provide access to Minecraft, in which case it would be called a "Minecraft server." In other cases, such as when a server serves a website, we refer to the server as a "web server." Who would've guessed?
Anyway, if you want to connect to a server, you can do so using either an IP address or a URL. An IP address is often difficult to read, which is why we use URLs. A URL points to an IP address and automatically (search "DNS" if you're curious about how) allows you to connect, just as if you were using the IP directly.
I've avoided going into the details of the TCP/IP stack layers to keep the explanation focused. I hope this clears up the difference between a server and a website! :)